From DE 199 35 960 A1, a clamping chuck for a tool comprising a device for supplying a coolant or lubricant from a spindle to a tool with a cooling channel is known. Furthermore, from TA 30 8243 01 of the company bielomatik LEUZE GmbH+Co, D-72637 Neuffen, such a clamping chuck is known. It can also be used as a clamping chuck for tools that have to be held in the clamping chuck at various depths and for this purpose are held by means of a shrink connection or by means of a hydro expansion chuck. Supplying a coolant or lubricant to the tool is by way of a sleeve that is firmly screwed to the chuck, to which sleeve lubricant is supplied by the spindle, wherein a tubular nozzle is pressed into this sleeve, which tubular nozzle conveys the lubricant onward to an adjusting screw. In this arrangement, the tubular nozzle or the tubular element is guided in the adjusting screw so as to be longitudinally slidable, and, by way of a rotary key, the adjusting screw is also longitudinally adjustable in the clamping chuck so that the adjusting screw can be rotated so as to contact the tool held in the clamping chuck. The adjusting screw is also used for manually setting the insertion depth of the tool, wherein for the purpose of rotating the adjusting screw, the tubular nozzle and the sleeve have to be deinstalled temporarily. Such temporary deinstallation is also necessary when the setting of the insertion depth takes place automatically with the use of a lance (see e.g. Inductive shrinking device GISS 3000 in the catalogue of the Gühring company: “Präzisions-Schneidwerkzeuge” (precision cutting tools) 2002 edition, page 958) in order to rotate the adjusting screw, following completion of the adjustment process, so that it contacts the tool so as to prevent turbulence in the coolant or lubricant flow in a free space between the adjusting screw and the tool. The state of the art is thus associated with a disadvantage in that the coolant supply arranged in the clamping chuck must be deinstalled and then reinstalled for each readjustment process that is required for the tool.